If the system of equations 3 x+ y+4 z=3 2 x+alpha y- z=-3 X+2 y+ z=4 has no solution, then the value of alpha is equal to:

for no solution Delta=0 |\ccc3 1 4 \ 2 alpha -1 \ 1 2 1\|=0 => 3( a+2)+1(-1-2)+4(4-alpha)=0 => 19-alpha=0 => alpha=19 \ for alpha=19 Delta_ x=|\ccc3 1 4 \ -3 19 -1 \ 4 2 1\|=3(21)+1(-1)+4(-82) ≠ 0 ∴ no solution for alpha=19

If the system of equations 3 x y 4 z 3 2 x alpha y z 3 ... | null (Mathematics)

JEE Mains 2026 21st January Shift 2

Mathematics

If the system of equations

\\3 \mathrm{x}+\mathrm{y}+4 \mathrm{z}=3\\

2 \mathrm{x}+\alpha \mathrm{y}-\mathrm{z}=-3\\

\mathrm{X}+2 \mathrm{y}+\mathrm{z}=4\\

has no solution, then the value of

\alpha

is equal to:

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Correct Answer:

Explanation

for no solution

\Delta=0\\

\left|\begin{array}{ccc}3 & 1 & 4 \\ 2 & \alpha & -1 \\ 1 & 2 & 1\end{array}\right|=0\\

\Rightarrow 3(\mathrm{a}+2)+1(-1-2)+4(4-\alpha)=0\\

\Rightarrow 19-\alpha=0 \Rightarrow \alpha=19\\

\& for

\alpha=19\\

\Delta_{\mathrm{x}}=\left|\begin{array}{ccc}3 & 1 & 4 \\ -3 & 19 & -1 \\ 4 & 2 & 1\end{array}\right|=3(21)+1(-1)+4(-82)\\

\neq 0\\

∴ no solution for

\alpha=19

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